Universal corrections to entanglement entropy of local quantum quenches

Abstract

We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, \epsilon. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order \epsilon^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the \epsilon^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential \mu. We calculate the time dependence of the order \epsilon^2 correction to the entanglement entropy for small \mu, and show that the contribution at order \mu^2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.Comment: References added, 56 pages, 9 figure

Time evolution of entanglement for holographic steady state formation

“…It is also interesting to note that the cases studied in [51,52] display a linear growth independent of the equation of state, showing more evidence that points towards a universal behavior. Related work on the evolution of entanglement entropy after a local quench also include [17][18][19][20][21][22][23][24][25]. In most of these references the authors complemented the holographic analysis with results from a CFT analysis.…”

“…In most of these references the authors complemented the holographic analysis with results from a CFT analysis. In particular in [21], the authors consider a local quench with a small time width and find universal features of the time evolution of the entanglement entropy.…”

“…For example, in the unphysical example (6.7) the curves span the intervals [1,4], [3,6] and [2,5]. 21 The first and the last of these intersect in [2,4] which is not one of the spanned intervals, hence this configuration is excluded as unphysical. In contrast, in the example (6.8) the curves span the set of intervals { [1,4], [2,3], [5,6]}, and apart from the empty interval the only intersection between these intervals is [2,3], which is an element of the above set.…”

“…21 Remember that the numbers 1 to 6 serve here as labels of (ordered) boundary points, and not necessarily as coordinates on the x-axis. Figure 19.…”

Subsystem distance after a local operator quench

“…In this paper, we consider the subsystem trace distance in latter category of quenches: at an initial time t = 0, a local operator is inserted somewhere in the ground state of the theory, and then the system is let evolve without further disturbance. The time evolution of entanglement and Rényi entropies, as well as of local operators, has been intensively studied in the literature [10][11][12][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The main goal of this paper is to investigate the distance between the RDMs at different times after a local operator quench.…”